The present invention relates to a method and apparatus for controlling a machine tool that performs circular interpolation control. More particularly, the present invention pertains to a method and apparatus for controlling a machine tool that performs high-precision cutting that is not achieved by a conventional circular speed restriction method.
New processing methods that use circular interpolation control have been expected to be developed in recent years. The processing methods include direct tapping, which forms a thread by a helical movement, orbit boring, which uses a single tool for forming several cylindrical bores having different diameters, and end milling, which does not use a boring bar. All the processing methods are aimed at improving the processing efficiency by reducing the number of times a tool must be exchanged. However, since the new methods do not excel over a conventional machining method, such as tapping and boring, in machining, the new methods have not replaced conventional methods. Circular interpolation control has been highly developed by technical improvements such as modification in the interpolation cycle and the interpolation unit of computer numerical control (CNC) and speeding up of a servo control process to obtain high gain. However, most of the circular interpolations used in the above machining methods are applied to a small diameter circle. Therefore, although the control technology has improved, the demanded accuracy is not easily achieved. Thus, there is a strong demand for improving the accuracy when controlling small diameter circular motion of a tool at a high speed.
As means for maintaining the accuracy of the circular interpolation, a method of restricting the feed rate is generally used to suppress the normal acceleration in circular motion to be less than or equal to a certain value. This method is effective for a contraction phenomenon of the arc radius caused mainly by tracking delay in the servo system. The contraction of arc radius is reduced by the improvement of the servo performance. However, the increased machining speed causes the normal acceleration in circular motion to act on the machine as a great inertia force. This results in a machine flexure, which significantly influences the accuracy of the circular interpolation. The phenomenon is particularly significant in the machining of a small circle and it is difficult to maintain the machining accuracy.
The conventional circular speed restriction method will now be described. The conventional circular speed restriction method is used to improve the machining accuracy when forming an arc or a perfect circle on a workpiece with a tool. The method controls the speed of the tool along the arc such that the acceleration of the tool does not exceed a certain value. The method is based on a theoretical arc radius reduction error amount ΔR (mm) obtained using the following equation (1) in accordance with the delay of position loop control.
                              Δ          ⁢                                          ⁢          R                =                                                            (                                  F                  60                                )                            2                                      2              ⁢              R                                ·                                    1              -                              K                f                2                                                    K              p              2                                                          (        1        )            
Where F represents the feed rate of the tool (mm/min), R represents the arc radius (mm), Kp represents position loop gain (S−1), and Kf represents the feedforward coefficient.
As the circular motion of the tool (feed rate F) increases, or the arc radius R is decreased, the acceleration is increased, which in turn increases the arc radius reduction error amount ΔR. Therefore, the conventional circular speed restriction method restricts the speed such that the acceleration does not exceed the upper limit to suppress the arc radius reduction error amount ΔR to be less than or equal to a certain value.
The method is effective if the main cause of the error in the circular track is delay from position loop control. In recent years, however, the feedforward coefficient Kf is set to a value close to one and delay from position loop control hardly occurs. According to the above equation (1), if the feedforward coefficient Kf is set to a value close to one, the right side of the equation (1) will be close to zero. Therefore, circular track error should not occur. However, in actual circular interpolation control, the demanded accuracy is not satisfied. This is because of a phenomenon different from that represented by the equation (1).
FIG. 7(a) shows the circularity (actual measurement) of the circular interpolation when the arc radius and the speed are varied. The horizontal axis represents the arc radius and the vertical axis represents the acceleration (square of the speed divided by the arc radius). Lines (constant circularity lines) in FIG. 7(a) are described by plotting points that represent a constant circularity when the arc radius and the acceleration are varied. If the circularity is proportional to the acceleration, each circularity line should extend parallel to the horizontal axis in FIG. 7 (a). However, in fact, the circularity deteriorates as the arc radius decreases as shown in FIG. 7(a).